GSEB Class 6 Maths Solutions Chapter 7 Fractions Exercise 7.2

Question 1. Draw number lines and locate the points on them:
(a) \( \frac { 1 }{ 2 }, \frac { 1 }{ 4 }, \frac { 3 }{ 4 }, \frac { 4 }{ 4 } \)
(b) \( \frac { 1 }{ 8 }, \frac { 2 }{ 8 }, \frac { 3 }{ 8 }, \frac { 7 }{ 8 } \)
(c) \( \frac { 2 }{ 5 }, \frac { 3 }{ 5 }, \frac { 8 }{ 5 }, \frac { 4 }{ 5 } \)
Answer:
(a) For the fractions \( \frac { 1 }{ 2 }, \frac { 1 }{ 4 }, \frac { 3 }{ 4 }, \frac { 4 }{ 4 } \), we first divide the section between 0 and 1 into 4 equal parts. We can write \( \frac { 1 }{ 2 } \) as \( \frac { 2 }{ 4 } \) for better comparison.From the figure, we observe:
Point B represents \( \frac { 1 }{ 4 } \).
Point C represents \( \frac { 1 }{ 2 } \) (which is \( \frac { 2 }{ 4 } \)).
Point D represents \( \frac { 3 }{ 4 } \).
Point E represents \( \frac { 4 }{ 4 } \) (which is 1).
(b) For the fractions \( \frac { 1 }{ 8 }, \frac { 2 }{ 8 }, \frac { 3 }{ 8 }, \frac { 7 }{ 8 } \), we divide the section between 0 and 1 into 8 equal parts.From the figure, we have:
Point B represents \( \frac { 1 }{ 8 } \).
Point C represents \( \frac { 2 }{ 8 } \).
Point D represents \( \frac { 3 }{ 8 } \).
Point H represents \( \frac { 7 }{ 8 } \).
(c) For the fractions \( \frac { 2 }{ 5 }, \frac { 3 }{ 5 }, \frac { 8 }{ 5 }, \frac { 4 }{ 5 } \), we divide the number line into parts of \( \frac { 1 }{ 5 } \). Since \( \frac { 8 }{ 5 } \) is an improper fraction, the number line should extend beyond 1.From the figure, we have:
Point B represents \( \frac { 2 }{ 5 } \).
Point C represents \( \frac { 3 }{ 5 } \).
Point H represents \( \frac { 4 }{ 5 } \).
Point D represents \( \frac { 8 }{ 5 } \).
In simple words: To locate fractions on a number line, first determine the denominator, which tells you how many equal parts to divide the space between whole numbers (like 0 and 1). Then, count the correct number of those parts from 0 to find the specific fraction. For improper fractions, you might need to extend the number line beyond 1.

Exam Tip: Always make sure your number line is evenly divided. Use a ruler and mark clear points for each fraction to avoid errors in placement.

Question 2. Express the following as mixed fractions.
(a) \( \frac { 20 }{ 3 } \)
(b) \( \frac {11}{5} \)
(c) \( \frac { 17 }{ 7 } \)
(d) \( \frac { 28 }{ 5 } \)
(e) \( \frac { 19 }{ 6 } \)
(f) \( \frac { 35 }{ 9 } \)
Answer:
(a) For \( \frac { 20 }{ 3 } \): \[ 3 ) 20 ( 6 \\ \quad -18 \\ \quad --- \\ \quad \quad 2 \] So, \( \frac { 20 }{ 3 } = 6 \frac { 2 }{ 3 } \)
(b) For \( \frac {11}{5} \): \[ 5 ) 11 ( 2 \\ \quad -10 \\ \quad --- \\ \quad \quad 1 \] So, \( \frac { 11 }{ 5 } = 2 \frac { 1 }{ 5 } \)
(c) For \( \frac { 17 }{ 7 } \): \[ 7 ) 17 ( 2 \\ \quad -14 \\ \quad --- \\ \quad \quad 3 \] So, \( \frac { 17 }{ 7 } = 2 \frac { 3 }{ 7 } \)
(d) For \( \frac { 28 }{ 5 } \): \[ 5 ) 28 ( 5 \\ \quad -25 \\ \quad --- \\ \quad \quad 3 \] So, \( \frac { 28 }{ 5 } = 5 \frac { 3 }{ 5 } \)
(e) For \( \frac { 19 }{ 6 } \): \[ 6 ) 19 ( 3 \\ \quad -18 \\ \quad --- \\ \quad \quad 1 \] So, \( \frac { 19 }{ 6 } = 3 \frac { 1 }{ 6 } \)
(f) For \( \frac { 35 }{ 9 } \): \[ 9 ) 35 ( 3 \\ \quad -27 \\ \quad --- \\ \quad \quad 8 \] So, \( \frac { 35 }{ 9 } = 3 \frac { 8 }{ 9 } \)
In simple words: To change an improper fraction into a mixed fraction, you need to divide the top number (numerator) by the bottom number (denominator). The whole number part of your answer is the quotient, the remainder becomes the new numerator, and the denominator stays the same.

Exam Tip: Remember that the denominator of the fractional part of a mixed number is always the same as the original denominator of the improper fraction. Only the numerator changes.

Question 3. Express the following as improper fractions:
(a) \( 7 \frac { 3 }{ 4 } \)
(b) \( 5 \frac {6}{7} \)
(c) \( 2 \frac {5}{6} \)
(d) \( 10 \frac { 3 }{ 5 } \)
(e) \( 9 \frac { 3 }{ 7 } \)
(f) \( 8 \frac { 4 }{ 9 } \)
Answer:
(a) For \( 7 \frac { 3 }{ 4 } \): We have: \( 7 \frac { 3 }{ 4 } = \frac { (7 \times 4) + 3 }{ 4 } = \frac { 28 + 3 }{ 4 } = \frac { 31 }{ 4 } \)
(b) For \( 5 \frac {6}{7} \): We have: \( 5 \frac { 6 }{ 7 } = \frac { (5 \times 7) + 6 }{ 7 } = \frac { 35 + 6 }{ 7 } = \frac { 41 }{ 7 } \)
(c) For \( 2 \frac {5}{6} \): We have: \( 2 \frac { 5 }{ 6 } = \frac { (2 \times 6) + 5 }{ 6 } = \frac { 12 + 5 }{ 6 } = \frac { 17 }{ 6 } \)
(d) For \( 10 \frac { 3 }{ 5 } \): We have: \( 10 \frac { 3 }{ 5 } = \frac { (10 \times 5) + 3 }{ 5 } = \frac { 50 + 3 }{ 5 } = \frac { 53 }{ 5 } \)
(e) For \( 9 \frac { 3 }{ 7 } \): We have: \( 9 \frac { 3 }{ 7 } = \frac { (9 \times 7) + 3 }{ 7 } = \frac { 63 + 3 }{ 7 } = \frac { 66 }{ 7 } \)
(f) For \( 8 \frac { 4 }{ 9 } \): We have: \( 8 \frac { 4 }{ 9 } = \frac { (8 \times 9) + 4 }{ 9 } = \frac { 72 + 4 }{ 9 } = \frac { 76 }{ 9 } \)
In simple words: To convert a mixed fraction back into an improper fraction, multiply the whole number by the denominator, then add the numerator. Place this new number over the original denominator.

Exam Tip: This process reverses the division you perform to get a mixed fraction, so always remember to multiply the whole number by the denominator first.